无迹卡尔曼滤波python代码

无迹卡尔曼滤波（Unscented Kalman Filter，UKF）是一种非线性滤波算法，用于估计系统状态。下面是一个简单的无迹卡尔曼滤波的Python代码示例：

import numpy as np

def unscented_kalman_filter(x, P, z, Q, R, f, h):
    n = len(x)
    m = len(z)

    # 参数设置
    alpha = 0.001
    beta = 2
    kappa = 0

    # Sigma点生成
    lambda_ = alpha**2 * (n + kappa) - n
    c = n + lambda_
    Wm = np.concatenate(([lambda_/c], np.ones(2*n)/2/c))
    Wc = np.concatenate(([lambda_/c+(1-alpha**2+beta)], np.ones(2*n)/2/c))
    sqrt_c = np.sqrt(c)

    # 预测步骤
    X = np.zeros((n, 2*n+1))
    X[:, 0] = x
    for i in range(n):
        X[:, i+1] = x + sqrt_c * np.linalg.cholesky(P)[:, i]
        X[:, n+i+1] = x - sqrt_c * np.linalg.cholesky(P)[:, i]

    X_pred = f(X)
    x_pred = np.dot(X_pred, Wm)
    P_pred = np.zeros((n, n))
    for i in range(2*n+1):
        P_pred += Wc[i] * np.outer(X_pred[:, i] - x_pred, X_pred[:, i] - x_pred)
    P_pred += Q

    # 更新步骤
    Z_pred = h(X_pred)
    z_pred = np.dot(Z_pred, Wm)
    Pz = np.zeros((m, m))
    for i in range(2*n+1):
        Pz += Wc[i] * np.outer(Z_pred[:, i] - z_pred, Z_pred[:, i] - z_pred)
    Pz += R

    Pxz = np.zeros((n, m))
    for i in range(2*n+1):
        Pxz += Wc[i] * np.outer(X_pred[:, i] - x_pred, Z_pred[:, i] - z_pred)

    K = np.dot(Pxz, np.linalg.inv(Pz))
    x = x_pred + np.dot(K, z - z_pred)
    P = P_pred - np.dot(K, np.dot(Pz, K.T))

    return x, P

# 示例函数f和h
def f(x):
    return np.sin(x)

def h(x):
    return x**2

# 初始化状态和协方差矩阵
x = np.array([0])
P = np.array([[1]])

# 测量数据
z = np.array([0.5])

# 过程噪声和测量噪声协方差矩阵
Q = np.array([[0.1]])
R = np.array([[0.1]])

# 执行无迹卡尔曼滤波
x_est, P_est = unscented_kalman_filter(x, P, z, Q, R, f, h)

print("估计的状态：", x_est)
print("估计的协方差矩阵：", P_est)

这段代码实现了一个简单的无迹卡尔曼滤波器，其中`f`和`h`分别表示状态转移函数和测量函数。你可以根据自己的需求修改这两个函数来适应不同的应用场景。